A and B are two magnitudes
where A is larger than B. How much larger? 
We set B alongside A and count off the number of times we use B to match A (its quantuplicity). Here B is used twice. 
We state the comparison as a ratio. Here we show the comparison of the two magnitudes, then write the ratio with their names. 
This gives a ratio: 
This is a proportion. Notice that it has two ratios and four terms (the four shapes). We can write the proportion with letters: 
We can then count the quantuplicity of the squares and write the ratio that appears on both sides of the '=' sign in the proportion: 
We can write the ratios of the sides as a proportion and then write the proportion in terms of measures (numbers). 
